into a rectangle could make two, two could do four in 3 would be 6 and so on. The question is: Describe how to find each "next nunber" of rectangles, without drawing the figure:
To find the number of rectangles in a given figure without explicitly drawing it, we need to understand the pattern involved.
Let's break down the pattern step by step:
1. Start with a single square:
- When you have just one square, there is only one rectangle in the figure.
2. Add another square horizontally:
- When you add a second square horizontally, it creates two new rectangles.
- These two rectangles are formed by pairing each side of the first square with each side of the second square.
3. Add a third square vertically:
- When you add a third square vertically, it creates three new rectangles.
- These three rectangles are formed by pairing each side of the first square with each side of the third square, excluding the connection between the second and third square.
4. Add a fourth square horizontally:
- When you add a fourth square horizontally, it creates four new rectangles.
- These four rectangles are formed by pairing each side of the first and second square with each side of the fourth square, excluding the connections between the second and third squares.
5. Continue adding squares and finding new rectangles:
- For each subsequent square added horizontally, you will create as many new rectangles as there are existing rectangles in the figure.
- For example, when adding a fifth square horizontally, you would create five new rectangles.
- When adding squares vertically, you will create one additional rectangle for each square added.
By following this pattern, you can find the number of rectangles in each subsequent figure without needing to draw it.